For linear regression, is an estimator of the variance of the dependent variable for a fixed x-value $SSE/(n-2)$?

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    $\begingroup$ You are assuming one independent variable and a constant term, right? $\endgroup$ – whuber Sep 23 '11 at 18:06
  • $\begingroup$ @whuber : yes I am. Is it correct then? Thanks. $\endgroup$ – user6478 Sep 23 '11 at 22:41
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    $\begingroup$ Technically any function of the data can be an estimator. Whether or not it is a good estimator is another matter. $\endgroup$ – Simon Byrne Sep 25 '11 at 16:40

Yes; you're looking for an estimate of the residual variance. See e.g. the wikipedia article on simple linear regression, though it's rather hidden there. I'd suggest a trip to the library, or buy a copy of Freedman et al, Statistics.

Also note that this is about $\text{var}(y) \cdot (1 - r^2)$.

  • $\begingroup$ The estimator is for $\text{var}(y) \cdot (1-r^2)$? This is the same thing as the residual variance right? $\endgroup$ – user6478 Sep 25 '11 at 14:28
  • $\begingroup$ @JamesErl Please register your account -- you will be able to post comments then. Just visit stats.stackexchange.com/users/login . $\endgroup$ – user88 Sep 25 '11 at 16:18
  • $\begingroup$ @JamesErl The variance of y for a fixed x is another way of saying residual variance. $\endgroup$ – Karl Sep 25 '11 at 16:31
  • $\begingroup$ @Karl Broman: So RMSE is basically the standard deviation of the difference in means of 2 populations? $\endgroup$ – Damien Sep 25 '11 at 16:40
  • $\begingroup$ @Damien No, I don't think that's at all related. $\endgroup$ – Karl Sep 25 '11 at 18:15

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